All sides being equal is a condition for congruency, not similarity. Similarity focuses on the ratio between rectangles and not on the equivalency of all sides. As for the statement regarding the equal angles, all rectangles regardless of similarity or congruency have four 90 degree angles. 

For two rectangles to be similar, their sides have to be proportional (form equal ratios). The ratio of the two longer sides should equal the ratio of the two shorter sides.

However, the left ratio in our proportion reduces.

We can then solve by cross multiplying.

We then solve by dividing.

For two rectangles to be similar, their sides must be in the same ratio.

This problem can be solved using ratios and cross multiplication. 

Let's denote the unknown width of the right rectangle as x. 

The goal is to solve for the height of the second rectangle. 

Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the height, we will be using this concept of ratios through solving for variables from the area.

First, it's helpful to achieve full dimensions for the first rectangle.

It is given that its base length is 5, and it has an area of 20. 

This means the first rectangle has the dimensions 5x4. 

Now, we may utilize the concept of ratios for similarity. The side lengths of the first rectangle is 5x4, so the second recatangle must have sides that are proportional to the first's.

We have the information for the first rectangle, so the data may be substituted in.

 is the ratio factor that will be used to solve for the height of the second rectangle. This may be substituted into the area formula for the second rectangle. 

Therefore, the height of the second rectangle is 10.

The goal of this problem is to figure out what base length of the second rectangle will make it similar to the first rectangle.

Similar rectangles function on proportionality - that is, the ratios of the sides between two rectangles will be the same. In order to determine the base, we will be using this concept of ratios through solving for variables from the perimeter.

First, all the dimensions of the first rectangle must be calculated.

This can be accomplished through using the perimeter equation: 

This means the dimensions of the first rectangle are 10x5. We will use this information for the ratios to calculate dimensions that would yield the second rectangle similar because of proprotions. 

 is the ratio factor we will use to solve for the base of the second rectangle. 

This will require revisiting the perimeter equation for the second rectangle.

Two rectangles are similar if their length and width form the same ratio. The small tile has a width of and a width of , providing us with the following ratio:

Since the length of similar triangles is twice their respective width, the length of the large tile can be determined as such:

To determine if these rectangles are similar, set up a proportion:

This proportion compares the ratio between the long sides in each rectangle to the ratio of the short sides in each rectangle. If they are the same, cross-multiplying will produce a true statement, and the rectangles are similar:

These rectangles aren't similar.

To determine if the rectangles are similar, set up a proportion comparing the short sides and the long sides from each rectangle: 

cross-multiply

since that's true, the rectangles are similar.

To find the scale factor, either divide 25 by 10 or 7.5 by 3. Either way you will get 2.5.

Two rectangles are similar if and only if their sides are in proportion. Specifically, 

Rectangle  Rectangle 

if 

Since  is located at the point , it follows that  and . Since  is located at the point , it follows that  and . Substituting in the aforementioned proportion statement, we get

.

Reducing to lowest terms, this is

.

This is false, so Rectangle  Rectangle .

Comparing the sides  and , we see that is  the length of , as shown here:

.

Since these two rectangles are similar, all pairs of corresponding sides are similar. Hence, the ratio of  to  is also , and we can calculate the length of  by setting up and solving a proportion:

.

Hence, the length of the side  is  units.